Over the weekend and during the R exams, I managed to complete the solution set for Chapters 6 and 7 of “Introducing Monte Carlo Methods with R”. Chapter 6 only exhibited a few typos, despite me covering most exercises in Chapter 6, hence the merging of both chapters.

– in Exercise 6.13, both and must use a double exponential proposal in the Metropolis-Hastings algorithm of question b,

in Exercise 6.15, the distribution should be a normal distribution,

– in Example 7.3, part of the code is wrong: it should be

> sigma2=theta=rep(0,Nsim)                  #init arrays
> sigma2[1]=1/rgamma(1,shape=a,rate=b)      #init chains
> B=sigma2[1]/(sigma2[1]+n*tau2)
> theta[1]=rnorm(1,m=B*theta0+(1-B)*xbar,sd=sqrt(tau2*B))

instead of

> sigma=theta=rep(0,Nsim)                  #init arrays
> sigma{1}=1/rgamma(1,shape=a,rate=b)      #init chains
> B=sigma2{1}/(sigma2{1}+n*tau2)
> theta{1}=rnorm(1,m=B*theta0+(1-B)*xbar,sd=sqrt(tau2*B))

(I frankly don’t understand where those curly brackets came from!)

– in Example 7.6, I forgot to include the truncation probability in the likelihood (!) and the notations are not completely coherent with Example 5.13 and 5.14 in that the x’s became y’s…

– in Exercise 7.21, rtnorm is missing sigma as one of its arguments.

– Exercise 7.23 has nothing wrong per se but it is rather a formal (mathematical) exercise

– in Exercise 7.25 the in question a should be to avoid any confusion.